Stage de pré-rentrée

θ
k∈Zθ∈R
cos(θ) sin(θ)
θ+kπ
cos(θ) sin(θ)
π
2+θπ 2−θ
cos(2θ) sin(2θ) cos(θ) sin(θ)θ
cos(p) + cos(q) sin(p) + sin(q)
p+q
2
p−q
2p q
cos(p) + sin(p)
x π t =tan x
2tsin(x)
cos(x)tan(x)
x∈[0,π
2[ cos(2x) = sin(6x)
x∈[0,2π[ cos(x)−√3 sin(x) = 1
n
X
i=1
i=n(n+ 1)
2
n
n
a b n ∈N∗
an−bn= (a−b)
n−1
X
k=0
akbn−k−1
∀a, b ∈R,|ab| ≤ a2+b2
2
∀a≥1,∀n∈N,(1 + a)n≥1 + na

∀x∈R,|sin(x)|≤|x|
∀x∈R, ex≥1 + x
∀x∈]−1,+∞[,ln(1 + x)≤x
(un)n∈N
un=
n
X
k=1
√k2+nk
n3+k2−k
(3 + 2i)(1 −i)−(2 + i)2
(1 + i)59−4i
2 + i
−2i1−i√3√3+3i
1 + i√3
√3 + i
λ∈Rz= (λ+i)(λ+ 5 −i(λ−7))
n∈N(1 + i)n
C2iz −z+ 4 −i=z−i2z+ (3 + i)z= 4 −i
f f(x) = 2
ex−1
g g(x) = cos(x)−cos2(x)
n∈NEn:xn+xn−1+... +x= 1
EnxnR+xn∈1
2,1
(xn)